In this paper we present a novel Code Execution Framework that can execute code of different problem solving environments (PSE), such as MATLAB, R and Octave, in parallel. In many e-Science domains different specialists are working together and need to share data or even execute calculations using programs created by other persons. Each specialist may use a different problem solving environment and therefore the collaboration can become quite difficult. Our framework supports different cloud platforms, such as Amazon Elastic Compute Cloud (EC2) and Eucalyptus. Therefore it is possible to use hybrid cloud infrastructures, e.g. a private cloud based on Eucalyptus for general base-level computations using the available local resources and additionally a public Amazon EC2 for peaks and time-dependent calculations. Our approach is to provide a secure platform that supports multiple problem solving environments, execute code in parallel with different parameter sets using multiple cores or machines in a cloud environment, and support researchers in executing code, even if the required problem solving environment is not installed locally. Additionally, existing parallel resources can easily be utilized for ongoing scientific calculations. The framework has been validated by and used in our real project addressing large-scale breath analysis research. Its research-prototype version is available as a PaaS cloud service model. In the future researchers will be able to install this framework on their own cloud infrastructures.